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<b>let </b><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">K</font> being  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a><br/> for <font color="Olive" title="b2">A</font>, <font color="Olive" title="b3">B</font> being  <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">K</font>  st <font color="Olive" title="b2">A</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Olive" title="b3">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Olive" title="b1">K</font>,<font color="Maroon" title="c1">n</font> holds <br/>( <font color="Olive" title="b2">A</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> &amp; <font color="Olive" title="b3">B</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> )</span><br/><b>let </b><font color="Maroon" title="c2">K</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being  <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">K</font>  st <font color="Olive" title="b1">A</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Olive" title="b2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font> holds <br/>( <font color="Olive" title="b1">A</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> &amp; <font color="Olive" title="b2">B</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> )</span><br/><b>let </b><font color="Maroon" title="c3">A</font>, <font color="Maroon" title="c4">B</font> be   <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">A</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font> implies ( <font color="Maroon" title="c3">A</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> &amp; <font color="Maroon" title="c4">B</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> ) )</span><br/>





<b>assume </b><a NAME="E1:63"/><i><font color="Green" title="E52">A1</font></i>: 
<font color="Maroon" title="c3">A</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">A</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> &amp; <font color="Maroon" title="c4">B</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> )</span><br/>

<b>consider </b><font color="Maroon" title="c5">B2</font> being   <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">K</font><b> such that </b><br/><a NAME="E3:63"/><i><font color="Green" title="E53">A5</font></i>: 
<font color="Maroon" title="c5">B2</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font>
 <b>by </b><i><a class="ref" href="matrix14.html#T55" target="_self" title="MATRIX14:th.55">AA4600</a>, <a class="txt" href="matrix14.html#E1:63"><i><font color="Green" title="E52">A1</font></i></a></i>;<br/>
<font color="Maroon" title="c5">B2</font> = 
<font color="Maroon" title="c5">B2</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font></span>)</span>
<b>by </b><i><a class="ref" href="matrix_3.html#T21" title="MATRIX_3:th.21">MATRIX_3:21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">B2</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c4">B</font>
<b>by </b><i><a class="ref" href="matrix14.html#T17" target="_self" title="MATRIX14:th.17">AA41</a>, <a class="txt" href="matrix14.html#E1:63"><i><font color="Green" title="E52">A1</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c4">B</font>
<b>by </b><i><a class="txt" href="matrix14.html#E3:63"><i><font color="Green" title="E53">A5</font></i></a>, <a class="ref" href="matrix_3.html#T20" title="MATRIX_3:th.20">MATRIX_3:20</a></i>
;<br/>
<a NAME="E5:63"/><b>then </b>
<font color="Maroon" title="c3">A</font> <a href="matrix_6.html#R2" title="MATRIX_6:pred.2">is_reverse_of</a> <font color="Maroon" title="c4">B</font>
 
<b>by </b><i><a class="ref" href="matrix_6.html#D2" title="MATRIX_6:def.2">MATRIX_6:def 2</a>, <a class="txt" href="matrix14.html#E1:63"><i><font color="Green" title="E52">A1</font></i></a>, <a class="txt" href="matrix14.html#E3:63"><i><font color="Green" title="E53">A5</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:63"/>
<font color="Maroon" title="c3">A</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>
 <b>by </b><i><a class="ref" href="matrix_6.html#D3" title="MATRIX_6:def.3">MATRIX_6:def 3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">B</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a></span><br/>

<b>consider </b><font color="Maroon" title="c6">B3</font> being   <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">K</font><b> such that </b><br/><a NAME="E8:63"/><i><font color="Green" title="E54">A5</font></i>: 
<font color="Maroon" title="c4">B</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c6">B3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font>
 <b>by </b><i><a class="ref" href="matrix14.html#T54" target="_self" title="MATRIX14:th.54">AA4500</a>, <a class="txt" href="matrix14.html#E1:63"><i><font color="Green" title="E52">A1</font></i></a></i>;<br/>
<font color="Maroon" title="c6">B3</font> = 
<span class="p1">(<span class="default"><a href="matrix_1.html#K12" title="MATRIX_1:func.12">1.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c6">B3</font>
<b>by </b><i><a class="ref" href="matrix_3.html#T20" title="MATRIX_3:th.20">MATRIX_3:20</a></i>
<br/>.= 
<font color="Maroon" title="c3">A</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c6">B3</font></span>)</span>
<b>by </b><i><a class="ref" href="matrix14.html#T17" target="_self" title="MATRIX14:th.17">AA41</a>, <a class="txt" href="matrix14.html#E1:63"><i><font color="Green" title="E52">A1</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c3">A</font>
<b>by </b><i><a class="txt" href="matrix14.html#E8:63"><i><font color="Green" title="E54">A5</font></i></a>, <a class="ref" href="matrix_3.html#T21" title="MATRIX_3:th.21">MATRIX_3:21</a></i>
;<br/>
<a NAME="E10:63"/><b>then </b>
<font color="Maroon" title="c4">B</font> <a href="matrix_6.html#R2" title="MATRIX_6:pred.2">is_reverse_of</a> <font color="Maroon" title="c3">A</font>
 
<b>by </b><i><a class="ref" href="matrix_6.html#D2" title="MATRIX_6:def.2">MATRIX_6:def 2</a>, <a class="txt" href="matrix14.html#E1:63"><i><font color="Green" title="E52">A1</font></i></a>, <a class="txt" href="matrix14.html#E8:63"><i><font color="Green" title="E54">A5</font></i></a></i>;<br/>
<b>hence </b><a NAME="E11:63"/>
<font color="Maroon" title="c4">B</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>
 <b>by </b><i><a class="ref" href="matrix_6.html#D3" title="MATRIX_6:def.3">MATRIX_6:def 3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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